Random Pursuit

Several Brownian Motions start either at the same place or apart by an initial distance. When do they bump into each other?
The 2-diemsional case is simulated here. The x-axis of the 2-d positions are projected to the bottom of the square, giving you a 1-d case. Two red BM starts at the same place, while the black BM start 40 pixles apart.

To prevent the applet from taking all the CPU times, the fastest pace is 100 steps per second.
On the bottom of the square there are three projections of the current positions of the Brownian motions.